time-cost tradeoff

One of the analysis that you should perform after
evaluating the resource allocation and leveling for your overall
project is to evaluate the impact of increasing or decreasing the
levels of resources, or their daily productivity. You might be
interested in the results of this analysis to decrease key
constraining activities such as power outages or to improve
productivity of leading production activities such as building
structural systems. During a project you may need to make-up for
delays experienced elsewhere on the project.

Take a moment and consider the types of actions you, as the
project manager, might be able to take to increase the total daily
productivity of planned work. Given a standard baseline of productivity
what would be the effect of increasing the productivity on the overall
cost of the project.

In the Time-Cost Tradeoff analysis you might consider overtime,
second shifts, or changing equipment to make some work proceed faster.
These additional resources, however, will often increase the cost of
the work, above a “standard” work day with the “typical” crew. If
all things are equal, there would be no consideration of increasing
productivity since any increase in cost of a fixed value project
would result in decreased profits. Since indirect costs are not
fixed, but are accrued each day on the project, it may be possible
to increase the cost of specific activities in order to decrease the
time of those activities. Decreasing the duration of those activities
may result in an overall decrease in project duration, and hence a
decrease on the overhead for job office, home office expenses.

Another reason to consider “buying time” through the Time-Cost?
Tradeoff analysis is to avoid liquidated damages penalties that
might be imposed for late projects. The expected increase in
profit due to early completion bonuses, widely used on urban
transportation projects, may also be evaluated through this method.

objective

The objective of the Time-Cost Tradeoff analysis is to determine
which activities to “crash” in order to produce the maximum overall
job profit. There are two parts to the analysis. First, as the
project duration decreases the cost of the project increases.
Second, the longer the project continues the higher the overhead
costs associated with the project. As demonstrated by the figure
below, the Time-Cost Tradeoff helps you to find the sweet-spot
between increasing costs of specific activities and decreasing overall
project costs.

step 1. normal and crash durations

To demonstrate the procedure for Time-Cost Tradeoff we will use
the small project, shown below. The four activities in this schedule
have a “normal” duration and cost and a “crash” duration and cost.
The normal duration reflects the original cost estimate and associated
duration for these activities. The crash duration shows the cost
of the activity if additional resources, overtime, or other special
measures were taken.

Activity

Prior

Normal

Crash

Duration

Cost

Duration

Cost

A

none

3

$2,000

1

$10,000

B

A

7

$4,000

3

$8,000

C

A

4

$2,000

2

$10,000

D

C

5

$3,000

2

$9,000

step 2. cost slope

For this example, let’s assume that there is a linear relationship
between the number of days that the activity is accelerated and the
increased cost associated with the activity. If we make this
assumption, then the cost of crashing each activity can be identified
by a line between the normal and crash duration. The slope of the
lines, shown below, reflects the cost of crashing each activity an
additional day.

For Activity A, the slope of the line between the normal and crashed
schedule would be ($10,000 - $2,000) / 1 – 3. The value of the slope
is -$4,000/day. The absolute value of the crash slope tells us that
we can crash Activity A at the cost of $4,000/day. If we want to
crash Activity A one day, then the new cost of Activity A will be the
normal cost of the activity, i.e. $2,000, plush one crash day cost,
i.e. $4,000, for a total of $6,000.

For a quick exercise, print out the table below and determine
the cost slope for each activity.

Activity

Prior

Normal

Crash

Cost Slope

Duration

Cost

Duration

Cost

A

none

3

$2,000

1

$10,000

B

A

7

$4,000

3

$8,000

C

A

4

$2,000

2

$10,000

D

C

5

$3,000

2

$9,000

step 3. fenced-bar chart

The first part of this task is to prepare the fenced bar chart.
After drawing the fenced bar chart there are two changes: (a)
write the cost slope of each activity above the bar; (b) inside the
activity bar shade the value of the totally crashed duration. If
you do this for the sample project you will see the following diagram.

step 4. iterate

Begin crashing activities starting with the least costly and
moving to the most costly. The cost to crash the entire schedule
will be based upon activities on the critical path. Look at the
previous bar chart and consider which activities might be crashed first.

To assist in the analysis you may draw a line through the activities
that must be crashed, to reduce the overall project duration. In
some cases you must crash more than one activity to decrease the
duration of the overall project. The figure below illustrates the
result of this process on our fenced bar-chart. Now that you know
what may be crashed, let’s determine what specific activities to crash
in which order.

On a scratch paper, list each of the possible crashed activities,
noting where multiple activities must be simultaneously crashed.
Identify the total cost slope for each set of crashed activities.
Sort the activity or set of activities in ascending order.

As you consider which activities to crash be sure to include only
those that will decrease the duration of the overall project. Look
at the example below. Will spending an extra $1,000 per day to speed
up Activity B alone decrease the duration of the project? Clearly not. As you select the
activities to crash, be sure that only those individual or combinations of
activities that decrease the project duration are selected for crashing.

The procedure for crashing the schedule is to begin by selecting
the activity or activities with the minimum total cost slope. Crash
those activities as much as possible with impacting any other activities.
Note the direct cost of that schedule and the duration of the resuling
project. Select the next least costly cost slope of activity or activities
and continue through the list of activities. For the purposes
of clarity, each step in the crash procedure is shown in the diagrams
below.

For the example project here are the activities to crash listed
in acending order by cost slope.

Crash Step

Activities to Crash

Crash Duration

Project Duration

Cost Slope

0

Normal Schedule

0

12

n/a

1

Crash D

2

10

$2,000/day

2

Crash B & D

1

7

$3,000/day

3

Crash A

2

7

$4,000/day

4

Crash B & C

2

5

$5,000/day

crash 0 - normal schedule

Activity

Duration

Direct Cost

A

3

$2,000

B

7

$4,000

C

4

$3,000

D

5

$3,000

Total Direct Cost

$11,000

crash 1 - crash D

Crash 1 - Crash D

Activity

Duration

Direct Cost

A

3

$0,000

B

7

$0,000

C

4

$0,000

D

3

$7,000

Total Direct Cost

$15,000

crash 2 - crash B & D

Crash 2 - Crash B & D

Activity

Duration

Direct Cost

A

3

$0,000

B

6

$5,000

C

4

$0,000

D

2

$9,000

Total Direct Cost

$18,000

crash 3 - crash A

Crash 2 - Crash A

Activity

Duration

Direct Cost

A

1

$10,000

B

6

$5,000

C

4

$0,000

D

2

$9,000

Total Direct Cost

$35,000

crash 4 - crash B & C

Crash 4 - Crash B & C

Activity

Duration

Direct Cost

A

1

$10,000

B

4

$6,000

C

2

$10,000

D

2

$9,000

Total Direct Cost

$37,000

Do you think that we should add another crash step
to fully compress the schedule? Why or why not?

step 4. time-cost tradeoff

While there is an increase in direct project costs resulting
from crashing the schedule, there is a decrease of indirect costs
associated with the project. In addition there may be bonus
payments for completing the project early. High indirect costs and
incentives make the use of the time-cost trade-off analysis a critical
project management tool.

Let’s consider the case where the cost providing the site
superintendant, etc… is $1,000/day. Let’s see what the indirect
and total project costs will be for each of the crashed schedules.

Project Duration

Direct Cost

Indirect Cost

Total Cost

Minimum

5

$35,000

$5,000

$40,000

7

$26,000

$7,000

$33,000

9

$18,000

$7,000

$27,000

10

$15,000

$10,000

$25,000

12

$11,000

$12,000

$23,000

<--

Here is the time-cost tradeoff chart for the example above.

Notice that having low jobsite overhead, a superintendant only,
keeps the project from having to be crashed to achieve a minimum
cost. If the contractor experiences a delay for which they have
to makeup time, i.e. crash some of the activities in the schedule,
the contractor has maximum flexibility in crashing low cost activities.

In the next example, let’s consider that the cost of a superintendent
trailer and phone is $2,000/day. The owner’s costs are also explicitly
included in the contract. In this example, the owner will charge the
contractor an additional $3,000/day for each day that the project is
late. As with all such penalties, the data after which these penalty
charges, or liquidated damages, occur is day eight (8). Let’s re-run
the numbers using the table below and see if there are any changes
in how we should plan to complete the project.

Project Duration

Direct Cost

Indirect Cost

Total Cost

Minimum

5

$35,000

$10,000

$45,000

7

$26,000

$14,000

$40,000

9

$18,000

$21,000

$39,000

<--

10

$15,000

$26,000

$41,000

12

$11,000

$36,000

$47,000

Here is the time-cost tradeoff chart for the example above.

In the situation with higher overhead and incentives (in this case
negative incentives, i.e. liquidated damages) The project should be
crashed 3 days to achieve the least costsly project. Note that although
the project will be completed one day past the owner's required time
of 8 days, that the cost to the contract is at it's minimum.